More Puzzles

you are an oil mogul considering the purchase of drilling rights to an as yet unexplored tract of land.
the well's expected value to its current owners is uniformly distributed over [$1..$100]. (i.e., a 1% chance it's worth each value b/w $1..$100, inclusive).
bcause you have greater economies of scale than the current owners, the well will actually be worth 50% more to you than to them (but they don't know this).
the catch: although you must bid on the well before drilling starts (and hence, before the actual yield of the well is known), the current owner can wait until *after* the well's actual value is ascertained before accepting your bid or not.
what should you bid?

Your bid must be made before the value is known; but it doesn't have to be accepted until after the value is known.

If your bid is less than the value to the current owner, it will be declined every time. If it is equal to or greater than the owner's expected gain, the bid will be accepted. (if the current owner refuses a bid with value exactly equal, it's impossible for you to make any money at all)

If you bid $1 and your bid is accepted (which it will be 1% of the time), you extract $1.50 worth of oil and net $.50. Expected gain from bidding $1 is $.005.

If you bid $2 and your bid is accepted, you expect to extract 2.25 worth of oil and net .25. Because your bid is accepted 2% of the time, the expected gain from bidding is still $.005.

If you bid $3 and the bid is accepted, you expect to extract $3 worth of oil. (There is an equal chance that the standard amount of oil is $1,$2,$3, and you get 1.5 times that, for an average of $3).

If you bid $4 or more, you expect strict loss.

Alternately, if bids other than a flat amount are allowed, you can bid 100% of the estimated value of oil.